<header>
    数学期望
</header>
<p>
    <span class="title">
        定义
    </span>
    设<span class="important">离散随机变量</span>X的分布列为
    <span class="oneline">
        p(x<sub>i</sub>)=P(X=x<sub>i</sub>), i=1,2,...,n,...
    </span>
    如果
    <span class="oneline">
        <code>
            ["sum","i=1","∞",""]
        </code>
        |x<sub>i</sub>|p(x<sub>i</sub>)＜∞
    </span>
    则称
    <span class="oneline">
        E(x) =
        <code>
            ["sum","i=1","∞",""]
        </code>
        x<sub>i</sub>p(x<sub>i</sub>)
    </span>
    为随机变量X的数学期望。
</p>
<p class="warn">
    特别说明：若级数
    <code>
        ["sum","i=1","∞",""]
    </code>
    |x<sub>i</sub>|p(x<sub>i</sub>)
    不收敛，则称X的数学期望不存在，下同类似，将不再赘述。
</p>
<p>
    <span class="title">
        定义
    </span>
    设<span class="important">连续随机变量</span>X的密度函数p(x)。如果
    <span class="oneline">
        <code>
            ["integral","|x|p(x)","dx","-∞","∞"]
        </code>
        ＜∞
    </span>
    则称
    <span class="oneline">
        E(x) =
        <code>
            ["integral","xp(x)","dx","-∞","∞"]
        </code>
    </span>
    为X的数学期望。
</p>